Spherical Nearfield Antenna Measurements
The subject of antenna measurements is one which has undergone revolutionary changes in recent years, in particular within space applications, where high demands are placed upon antenna design and construction. This book represents the specific measurement technique known as the spherical nearfield method. The theoretical treatment of the method is detailed but of sufficient generality to make the book useful as a basis for further research on nearfield measurements and antenna coupling problems. Practical aspects of antenna test ranges, data processing schemes and measurement procedures are described. Other topics covered are measurement error analysis and generation of plane wave fields. The authors draw on the experience from the development, sponsored by the European Space Agency, of one of the first spherical nearfield test ranges. They have contributed to the establishment of spherical nearfield testing as a highly accurate and versatile method, currently under implementation at test ranges worldwide.
Other keywords: antenna coupling; error analysis; nearfield antenna measurement; plane wave synthesis; spherical wave; scattering matrix
 Book DOI: 10.1049/PBEW026E
 ISBN: 9780863411106
 eISBN: 9781849193849
 Page count: 404
 Format: PDF

Front Matter
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1 Introduction
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A need for precise measurement of the radiation from microwave antennas has arisen in connection with the development of advanced antenna design concepts and improved theoretical approaches for antenna analysis. The need has been felt in particular within space applications where antennas are being constructed to tight specifications, i.e. down to the order of one per cent in gain. Antenna testing has therefore attracted considerable interest in recent years where a large number of studies have been made and new developments effected. The oldest type of test range, the outdoor farfield range, has seen a few modern implementations. However, it is to the indoor test techniques that most of the efforts have been devoted. The compact range as well as nearfield scanning ranges in planar, cylindrical and spherical geometries have all more or less reached mature states. They are now being installed at many places and seem to be the natural choice for contemporary antenna testing.

2 Scattering matrix descriptionof an antenna
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Scattering matrix theory plays an important role in connection with spherical nearfield testing. Firstly, the theory is convenient for the derivation of a 'spherical' transmission formula. Here, it is not required that the test antenna and the probe are both reciprocal antennas. Reciprocity, if present, is expressed conveniently as a relationship between elements of the scattering matrix. Secondly, scattering matrix theory provides the link between quantities measurable in transmission lines and external fields without reference to particular structural types. The theory constitutes a means for absolute measurements of electromagnetic fields without unknown or unspecified constants. The present chapter begins with a description of spherical wave theory in sufficient detail for the purpose of a comprehensive treatment in later chapters of the theoretical sides of spherical nearfield antenna measurements without probe correction and with probe correction. The presentation of spherical waves is traditional, however with a new and simplified notation for the wave functions.

3 Scattering matrix description ofantenna coupling
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The scattering matrix theory for antennas is the obvious tool for analyzing the interaction between the test antenna and the probe in near field test ranges with spherical geometries. In particular, the theory forms a natural basis for a simple derivation of the transmission formula in spherical coordinates. This formula is fundamental to spherical nearfield testing of antennas, and its derivation is the main subject of this chapter.

4 Data reduction in spherical nearfield measurements
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This chapter considers a measurement setup in which the test antenna transmits and the probe receives. The required data processing for obtaining the test antenna transmitting coefficients and subsequently the radiated field is then the subject of this chapter. Two different theoretical approaches are possible: measurement with and without probe correction.

5 Measurements
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This chapter deals with the practical aspects of spherical nearfield antenna testing. Section 5.2 on measurement probes provides a transition from the theoretical chapters to the experimental techniques beginning in Section 5.3. Section 5.3 on probe corrected measurements contains a section (5.3.2) where the spherical nearfield test range is examined from a system point of view. In another section (5.3.3), the test range is described from the point of view of the various measurement procedures that can be carried out on the range and that constitute a complete measurement of a given test antenna. Some measurement results obtained at the TUD test range are also presented (Section 5.3.4). As was shown in Chapter 4, the basic spherical nearfield measurement not only yields the radiation patterns of the test antenna but also its directivity. If the test antenna gain is wanted, some additional measurements must be carried out. These are dealt with in Section 5.4.

6 Error analysis of spherical nearfield measurements
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Nearfield testing involves a numerical transformation of the measured data to the far field of the antenna. Thus, the influence of measurement inaccuracies may be found difficult to evaluate directly and it may be an advantage to apply computer simulations of the measurements. The principle and results of simulations for the spherical technique are presented in the following sections. The influence of probe correction is analyzed and the effects of truncation of the measurement sphere will be considered. Finally, simulated inaccuracies are compared to inaccuracies of real measurements.

7 Planewave synthesis
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This chapter considers the general problem of farfield measurements from the point of view of planewave synthesis. This point of view is straightforward if we consider the measurement of the receiving characteristics of a test antenna. The farfield pattern can here be measured with the receiving test antenna rotated in an incident planewave field. Any deviation from planewave behaviour of the incident field in the volume occupied by the test antenna  caused, for example, by compromises in the design of the range, reflections from surroundings or multiple interaction  will cause errors in the measured farfield data. Arguments of this kind show that any farfield measurement technique must, in some way, realize or synthesize a quasiplane wave field in the test zone. The creation of a planewave zone of sufficient quality can be achieved in a number of different ways which may be used to classify the various types of farfield measurement ranges. The quality of the planewaves produced allows comparison of the different ranges.

Appendix 1: Spherical wave functions,notation and properties
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Electromagnetic fields may be expanded into spherical waves in sourcefree regions of space limited by spherical surfaces centred at the origin of a spherical coordinate system (r, θ, Φ).

Appendix 2: Rotation of spherical waves
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Considers two righthanded rectangular coordinate systems, initially co incident. Let the first, the unprimed system (x, y, z), remain fixed in space while the other, the primed system (x', y', z'), is rotated about the origin from its initial orientation to some arbitrary orientation in space and kept there.

Appendix 3: Translation of spherical waves
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Considers two righthanded rectangular coordinate systems, initially coincident. Let the first, the unprimed system (x, y, z), remain fixed in space while the other, the primed system, is translated a distance A in the positive direction of the zaxis; Here, we shall consider the spherical coordinate systems defined in the usual manner with respect to the rectangular systems.

Appendix 4: Data processing in antenna measurements
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In antenna pattern measurements in general and in spherical nearfield testing in particular extensive use is made of various forms of sampling and reconstruction schemes for bandlimited, periodic functions. The purpose of this appendix is to provide an overview of these techniques.

Appendix 5: List of principal symbols and uses
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Back Matter
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Supplementary material

Errata for 'Spherical NearField Antenna Measurements'

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